Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (4): 1153-1166.doi: 10.1016/S0252-9602(16)30060-1

• Articles • Previous Articles     Next Articles

A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

Huihui KONG1, Hai-Liang LI1, Xingwei ZHANG2   

  1. 1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
    2 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2015-11-14 Revised:2016-01-29 Online:2016-08-25 Published:2016-08-25
  • Contact: Hai-Liang LI,E-mail:hailiang.li.math@gmail.com E-mail:hailiang.li.math@gmail.com
  • Supported by:

    The research of the authors is supported by the NNSFC (11171228, 11231006, and 11225102), NSFC-RGC Grant 11461161007, and the Key Project of Beijing Municipal Education Commission No. CIT&TCD20140323.

Abstract:

In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.

Key words: Blow-up criterion, spherically symmetric, free boundary, compressible Navier-Stokes equations

CLC Number: 

  • 35B44
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